Carsten:
I vaguely remember being asked for my personal number when registering my car but I'm afraid that I can't remember how it was resolved, but it was. You should definitely be able to have it registered in your own name.
Hopefully, someone with a better memory than mine will reply to you.

Re Tierra Del Sol requiring an Aruban ID, they should be able to tell you how to deal with it as I'm sure this has come up with them before.
Good luck!